What criteria do people use to decide if a theory in physics is successful?
For special relativity, general relativity, and quantum theory, highly precise measurements can be performed and compared to predictions of the theory. For example, Quantum Electrodynamics (QED) gives a value for the magnetic moment of the electron that agrees with experiment, to within one part in a trillion. However, for complex systems and emergent properties we do not have the luxury of such clear-cut criteria for deciding the success of a theory.
Almost everyone would agree that the BCS theory of superconductivity is a smashing success. But it cannot predict whether a specific material is a superconductor. Its best predictions for elemental superconductors agree with experiment within a few per cent. Nevertheless, BCS is deemed successful because it gives a quantitative description of a wide range of thermodynamic, transport, and NMR properties for diverse materials. BCS is also consistent with Ginzburg-Landau theory and can be justified by more microscopic theories.
But not everyone was a fan of BCS. Bernd Matthias (1918-1980) discovered hundreds of elements and alloys that were superconductors. Yet, he was a vocal critic of BCS.
For cuprate superconductors, there is no consensus as to what the best current theory is. This arguably partly arises because different people use different criteria to evaluate the available theories.
There is a stimulating article, Understanding complexity, by Sophia Kivelson and Steven Kivelson
They state: "The criteria by which the validity of theories of complex systems are judged are more nuanced than a naive understanding of ‘the scientific method’ suggests."
They suggest that a successful theory must incorporate at least two features:
it explicitly identifies which features of the system need to addressed
it has a great degree of knowledge compression.
These features are in addition to criteria of precision, accuracy, and utility.
Related issues have been discussed in detail and beautifully in the theoretical chemistry context by Hoffmann and Malrieu.
The complexity of these issues for emergent properties is accentuated because there are four types of theories: phenomenology, effective theories, toy models, and microscopic theories. (See Section 4.5 in my review article). The criteria for evaluation of each type will be different and subjective. Furthermore, the criteria will vary depending on the specific scientific discipline or sub-field concerned.
What do you think? What criteria should be used to evaluate theories of emergent properties?
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